4 0 -2 n- 6. 2 5 4 23. 0 0 5 -2 0 -1 [5 0 0 0 0 0 1 2 0 0 2 1 4 1 0 0 0 0 4 -1 0 -2 Diagonalize the matrices in Exercises 7-20, if possible. The eigenvalues for Exercises 11-16 are as follows: (11) A = 1,2,3 (12) A - 2,8; (13) A = 5, 1 ; (14) A = 5, 4; (15) A = 3, 1; (16) = 2, 1. For Exercise 18, one eigenvalue is A = 5 and one eigenvector is (-2, 1, 2). 2 10. 4 3 25. A is 2 4 0 12. Ju 3 2 26. А 1 tv 0 -2 di 1 14. 2 5 4 Ju 2 0 0 5 27. S 16 0 -4-6 is 8 16. 0 -3 -1 28. S -5 1 2 SC -7 -16 4 29. A 18. 6 13 -2 fo 16 12 1 th 0 4 0 A 0 0 4 0 20. 0 -2 0 2 0 0 30. W br# 2 0 0 2 to 31. Co 22, A, B, P, and D are n xn matrices. True or False. Justify each answer. (Study dia 224 2 4 2 2
4 0 -2 n- 6. 2 5 4 23. 0 0 5 -2 0 -1 [5 0 0 0 0 0 1 2 0 0 2 1 4 1 0 0 0 0 4 -1 0 -2 Diagonalize the matrices in Exercises 7-20, if possible. The eigenvalues for Exercises 11-16 are as follows: (11) A = 1,2,3 (12) A - 2,8; (13) A = 5, 1 ; (14) A = 5, 4; (15) A = 3, 1; (16) = 2, 1. For Exercise 18, one eigenvalue is A = 5 and one eigenvector is (-2, 1, 2). 2 10. 4 3 25. A is 2 4 0 12. Ju 3 2 26. А 1 tv 0 -2 di 1 14. 2 5 4 Ju 2 0 0 5 27. S 16 0 -4-6 is 8 16. 0 -3 -1 28. S -5 1 2 SC -7 -16 4 29. A 18. 6 13 -2 fo 16 12 1 th 0 4 0 A 0 0 4 0 20. 0 -2 0 2 0 0 30. W br# 2 0 0 2 to 31. Co 22, A, B, P, and D are n xn matrices. True or False. Justify each answer. (Study dia 224 2 4 2 2
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
I am confused with how to find the general solution of the matrix for problem 14. In this problem the general solution matrix is [-1/2 1 0],but I don't understand why that would be the general solution.
Transcribed Image Text:4
0 -2
n-
6.
2
5
4
23.
0
0 5
-2
0 -1
[5 0
0
0 0
0
1
2
0
0
2
1
4
1
0
0
0
0
4
-1 0
-2
Diagonalize the matrices in Exercises 7-20, if possible. The
eigenvalues for Exercises 11-16 are as follows: (11) A = 1,2,3
(12) A - 2,8; (13) A = 5, 1 ; (14) A = 5, 4; (15) A = 3, 1; (16)
= 2, 1. For Exercise 18, one eigenvalue is A = 5 and one
eigenvector is (-2, 1, 2).
Transcribed Image Text:2
10.
4
3
25. A
is
2
4
0
12.
Ju
3
2
26. А
1
tv
0
-2
di
1
14.
2
5
4
Ju
2
0
0
5
27. S
16
0 -4-6
is
8
16.
0 -3
-1
28. S
-5
1 2
SC
-7
-16
4
29. A
18.
6
13 -2
fo
16
12
1
th
0
4
0
A
0
0
4
0
20.
0
-2
0
2
0
0
30. W
br#
2
0 0
2
to
31. Co
22, A, B, P, and D are n xn matrices.
True or False. Justify each answer. (Study
dia
224
2 4 2
2
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